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Statistical Inference Procedures for Bivariate Archimedean Copulas.
- Source :
-
Journal of the American Statistical Association . Sep93, Vol. 88 Issue 423, p1034-1043. 10p. 6 Charts, 2 Graphs. - Publication Year :
- 1993
-
Abstract
- A bivariate distribution function H(x, y) with marginals F(x) and G(y) is said to be generated by an Archimedean copula if it can be expressed in the form H(x, y) = φ-1[φ{F(x)} + φ{G(y)}] for some convex, decreasing function φ defined on (0, 1] in such a way that φ(1) = 0. Many well-known systems of bivariate distributions belong to this class, including those of Gumbel, Ali-Mikhail-Haq-Thélot, Clayton, Frank, and Hougaard. Frailty models also fall under that general prescription. This article examines the problem of selecting an Archimedean copula providing a suitable representation of the dependence structure between two variates X and Y in the light of a random sample (X1, Y1), ,(Xn, Yn) The key to the estimation procedure is a one-dimensional empirical distribution function that can be constructed whether the uniform representation of X and Y is Archimedean or not, and independently of their marginals. This semiparametric estimator, based on a decomposition of Kendall's tau statistic, is seen to be √n-consistent, and an explicit formula for its asymptotic variance is provided. This leads to a strategy for selecting the parametric family of Archimedean copulas that provides the best possible fit to a given set of data. To illustrate these procedures, a uranium exploration data set is reanalyzed. Although the presentation is restricted to problems revolving a random sample from a bivariate distribution, extensions to situations involving multivariate or censored data could be envisaged. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01621459
- Volume :
- 88
- Issue :
- 423
- Database :
- Academic Search Index
- Journal :
- Journal of the American Statistical Association
- Publication Type :
- Academic Journal
- Accession number :
- 9312090750
- Full Text :
- https://doi.org/10.1080/01621459.1993.10476372